Abstract

In this paper, a novel non-asymptotic method for target localization based on the algebra of Volterra linear integral operators is presented aiming at estimating the coordinate of a stationary source by a single mobile agent. The algorithm assumes that the agent is only allowed to obtain the measurement of distance from the source. By properly designing the kernel of the Volterra operators, the influence of initial conditions on the transient phase can be eliminated in order to achieve - ideally - a deadbeat mode of behavior. The stability analysis shows that the algorithm is robust to bounded additive measurement perturbations. Moreover, the bias on the estimate due to time-discretization is characterized. Simulation results show that the proposed algorithm is characterized by fast convergence and good noise immunity.

Highlights

  • The problem of target localization represents one of the fundamental issues in several engineering fields such as aerospace, military, wireless sensor networks, etc

  • The localization systems can be classified into two categories: the global positioning systems (GPS) and the local positioning system (LPS) [2]

  • Volterra integral operators play a key role in transforming a differential expression into a sequence of algebraic equations

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Summary

INTRODUCTION

The problem of target localization represents one of the fundamental issues in several engineering fields such as aerospace, military, wireless sensor networks, etc. A robust correctionbased state estimator is designed with the consideration of disturbances on both the distance measurement and velocity Another family of approaches is based on regression formulation derived from geometrical relationship (see [15], [16], [17], [18]). Besides the aforementioned linear estimation frameworks, in our recent work [21], Volterra integral operators have been applied to the nonlinear range-based localization problem, yielding the position estimation of a fixed target in a deadbeat manner in the ideal case. The robust stability analysis provides evidence that the estimation error remains bounded in case of a persistently drifting target and measurement noise, making the proposed algorithm a viable choice for the practical implementation.

PROBLEM STATEMENT AND PRELIMINARIES
NON-ASYMPTOTIC VOLTERRA OPERATORS ALGEBRA
Dynamic implementation of Volterra operators
Kernel conditions for non-asymptoticity
A KERNEL-BASED NON-ASYMPTOTIC LOCALIZATION ALGORITHM
Stability analysis
Analysis of the bias introduced by the time-discretization of the algorithm
DRIFTING TARGET
SIMULATION RESULTS AND COMPARISONS
Stationary target: estimation under noise-free condition
Stationary target: estimation in noisy scenario
Drifting target: estimation under noise-free condition
Drifting target: estimation in noisy scenario
VIII. CONCLUDING REMARKS
Methods
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